In: Bretar F, Pierrot-Deseilligny M, Vosselman G (Eds) Laser scanning 2009, IAPRS, Vol. XXXVIII, Part 3/W8 – Paris, France, September 1-2, 2009
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CLUSTERING OF LIDAR DATA USING PARTICLE SWARM OPTIMIZATION
ALGORITHM IN URBAN AREA
F. Samadzadegan, S. Saeedi
Dept. of Geomatics, Faculty of Engineering, University of Tehran, Tehran, Iran, (samadz, ssaeedy)@ut.ac.ir
KEY WORDS: Clustering, LIDAR, Particle swarm optimization, Urban Area, Object Extraction
ABSTRACT:
One of the fundamental steps in the transformation of the LIDAR data into the meaningful objects in urban area involves their
segmentation into consistent units through a clustering process. Nevertheless, due to the scene complexity and the variety of objects
in urban area, e.g. buildings, roads, and trees, it is clear that a clustering using only a single cue will not suffice. Considering the
availability of additional data sources, like laser range and intensity information in both first and last echo, more information can be
integrated in the clustering process and ultimately into the recognition and reconstruction scheme. Multi dimensionality nature of
LIDAR data with a dense sampling interval in urban area generates a huge amount of information. This amount of information has
produced a lot of problems for finding global optima in most of traditional clustering techniques. This paper describes the potential
of a Particle Swarm Optimization (PSO) algorithm to find global solutions to the clustering problem of multi dimensional LIDAR
data in urban area. It is a kind of swarm intelligence that is based on social-psychological principles and provides insights into social
behaviour, as well as contributing to engineering applications. By integrating the simplicity of the k-means algorithm with the
capability of the PSO algorithm, this paper presents a robust and efficient clustering method which can overcome the problem of
trapping to local optima of k-means technique. This algorithm successfully applied to clustering of several LIDAR data sets in
different urban area with different size and complexities. The experimental results demonstrate that PSO based clustering technique
produces much better outputs in terms of both accuracy and computation time than other traditional clustering techniques.
enlarge the size of data sets and proportionally the dimension
of feature spaces in clustering process. As a result, most of
traditional clustering techniques that have been applied
properly in other applications with standard data and feature
space dimension are not efficient enough for object extraction
process from LIDAR data (Lodha et al., 2007).
1. INTRODUCTION
LIDAR has become a standard data collection technology for
capturing object surface information in 3D modelling of urban
area. Although, these systems provide detailed valuable
geometric information, but still require interpretation of the data
for object extraction and recognition to make it practical for
mapping purposes. During last decade, several numbers of
clustering and filtering techniques have been developed to
recognition of the objects for 3D city modelling or removing the
“artefacts” of bare terrain (Maas, 2001; Tao and Hu, 2001;
Filin, 2002; Rottensteiner and Briese, 2002; Sithole and
Vosselman, 2003; Samadzadegan, 2004; Vosselman et al.,
2004; Lodha et al., 2007; Sampath and Shan, 2008).
k-means is one of the most popular clustering algorithms,
which could be consider for handling the massive datasets.
The algorithm is efficient at clustering large data sets because
its computational complexity only grows linearly with the
number of data points (Kotsiantis and Pintelas, 2004).
However, the algorithm may converge to solutions that are not
optimal. In this paper, an alternative clustering method to
solve the local optimum problem of the k-means algorithm is
presented. The applied method adopts the particle swarm
optimization algorithm as it has proved to give a more robust
performance than other intelligent optimisation methods for a
range of complex problems.
In order to improve the performance of 3D object extraction
process, additional data has been considered. First, LIDAR
systems register two echoes of the laser beam, the first and the
last pulse, generally corresponding to the highest and the lowest
object point hit by the laser beam. First and last pulse data will
especially differ in the presence of vegetation (Kraus, 2002).
Moreover, LIDAR systems record the intensity of the returned
laser beam which is mainly in the infrared part of the
electromagnetic spectrum. Nevertheless, the intensity image is
under-sampled and, thus, very noisy. In addition, an extra
powerful source of information is visible images. Digital images
can provide necessary information due to their intensity and
spectral content as well as their high spatial resolution which is
still better than the resolution of laser scanner data.
2. BASIC CONCEPTS IN DATA CLUSTERING
Historically the notion of finding useful patterns in data has
been given a variety of names including data clustering, data
mining, knowledge discovery, pattern recognition, information
extraction, etc (Ajith et al., 2006). Data clustering is an
analytic process designed to explore data in discovering of
consistent patterns and/or systematic relationships between
variables, and then to validate the findings by applying the
detected patterns to new subsets of data.
Therefore, in the context of 3D object extraction in urban area,
various type of information has been fused to overcome the
difficulties of classification and identification of complicated
objects (Lim and Suter, 2007; Morgan and Habib, 2002;
Vosselman et al., 2004). Collecting this information, extremely
Generally, clustering algorithms can be categorized into
partitioning methods, hierarchical methods, density-based
methods, grid-based methods, and model-based methods. An
334
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excellent survey of clustering techniques can be found in
(Kotsiantis and Pintelas, 2004). In this paper, the focus will be
on the partitional clustering algorithms because they are more
popular than other clustering algorithms in clustering of
remotely sensed data (Harvey et al., 2002; Omran et al., 2005;
Wilson et al., 2002). Partitional clustering algorithms divide the
data set into a specified number of clusters and then evaluate
them by some criterion. These algorithms try to minimize
certain criteria (e.g. a square error function) and can therefore
be treated as optimization problems.
More recently, Paterlini and Krink (2005) compared the
performance of k-means, GAs, PSO and Differential Evolution
(DE) for a representative point evaluation approach to
partitional clustering. The results show that GAs, PSO and DE
outperformed the k-means algorithm. Pham et al. (2006) used
the bee algorithm for clustering of different data sets. The
obtained results of their work show that their proposed bee
algorithm has better performance than both of standard kmean as well as GA-based method. In general, the literature
review of recent techniques in the background of clustering
shows that the swarm-based clustering algorithm performs
better than the k-means algorithm.
The most widely used partitional algorithm is the iterative kmeans approach (Kotsiantis and Pintelas, 2004). The k-means
algorithm starts with k centroids (initial values are randomly
selected or derived from a priori information). Then, each
pattern in the data set is assigned to the closest cluster (i.e.
closest centroid). Finally, the centroids are recalculated
according to the associated patterns. This procedure is repeated
until convergence is achieved.
Regarding to the recent researches in the context of clustering
of massive LIDAR data and unique potential of PSO
algorithm in solving complex optimization, a clustering
algorithm based on Particle Swarm Optimization (PSO) for
outperforming k-mean method is developed in this paper.
3.1 Particle Swarm Optimization
It is known that the k-means algorithm may become intent at
local optimal solutions, depending on the choice of the initial
cluster centres. Genetic algorithms have a potentially greater
ability to avoid local optima than is possible with the localised
search employed by most clustering techniques. Maulik and
Bandyopadhyay (2004) proposed a genetic algorithm-based
clustering technique, called GA-clustering, that has proven
effective in providing optimal clusters. With this algorithm,
solutions (typically, cluster centroids) are represented by bit
strings.
The PSO method is one of optimization methods developed
for searching global optima of a nonlinear function (Kennedy
and Eberhart, 1995; Kennedy et al., 2002). It is inspired by the
social behaviour of birds and fish. The method uses group of
problem solutions. Each solution consists of set of parameters
and represents a point in multidimensional space. Each
potential solution is called particle and the group of particles
(population) is called swarm. Particles move through the
search domain with a specified velocity in search of optimal
solution. Each particle maintains a memory which helps it in
keeping the track of its previous best position. The positions of
the particles are distinguished as personal best and global best.
PSO has been applied to solve a variety of optimization
problems and its performance is compared with other popular
stochastic search techniques like Genetic algorithms,
Differential Evolution, Simulated Annealing etc. (Kennedy et
al., 2002; Omran and Engelbrecht, 2005).
The search for an appropriate solution begins with a population,
or collection, of initial solutions. Members of the current
population are used to create the next generation population by
applying operations such as random mutation and crossover. At
each step, the solutions in the current population are evaluated
relative to some measure of fitness, with the fittest solutions
selected probabilistically as seeds for producing the next
generation. The process performs a generate-and-test beam
search of the solution space, in which variants of the best
current solutions are most likely to be considered next.
The working of the PSO may be described as: For a Ddimensional search space the position of the ith particle is
represented as Xi = (xi1, xi2, … xiD). Each particle maintains a
memory of its previous best position Pbest = (pi1, pi2… piD).
The best one among all the particles in the population is
represented as Pgbest = (pg1, pg2… pgD). The velocity of each
particle is represented as Vi = (vi1, vi2, … viD). In each
iteration, the P vector of the particle with best fitness in the
local neighbourhood, designated g, and the P vector of the
current particle are combined to adjust the velocity along each
dimension and a new position of the particle is determined
using that velocity. The two basic equations which govern the
working of PSO are that of velocity vector and position vector
given by:
3. CLUSTERING OF LIDAR DATA USING PSO
ALGORITHM
Swarm Intelligence (SI) is an innovative distributed intelligent
paradigm for solving optimization problems that originally took
its inspiration from the biological examples by swarming,
flocking and herding phenomena in vertebrates. These
techniques incorporate swarming behaviours observed in flocks
of birds, schools of fish, or swarms of bees, and even human
social behaviour, from which the idea is emerged (Omran et al.,
2002, 2005; Paterlini and Krink, 2005; Pham et al., 2006; Wu
and Shi, 2001). Data clustering and Swarm intelligence may
seem that they do not have many properties in common.
However, recent studies suggest that they can be used together
for several real world data clustering and mining problems
especially when other methods would be too expensive or
difficult to implement.
1
(1)
1
1
(2)
The first part of equation (1) represents the inertia of the
previous velocity, the second part is the cognition part and it
tells us about the personal experience of the particle, the third
part represents the cooperation among particles and is
therefore named as the social component. Acceleration
constants c1, c2 and inertia weight w are the predefined by the
user and r1, r2 are the uniformly generated random numbers in
the range of [0, 1].
Clustering approaches inspired by the collective behaviours of
ants have been proposed by Wu and Shi (2001), Labroche et al.
(2001). The main idea of these approaches is that artificial ants
are used to pick up items and drop them near similar items
resulting in the formation of clusters. Omran et al. (2002)
proposed the first PSO-based clustering algorithm. The results
of Omran et al. (2002, 2005) show that PSO outperformed kmeans, FCM and other state-of-the-art clustering algorithms.
335
In: Bretar F, Pierrot-Deseilligny M, Vosselman G (Eds) Laser scanning 2009, IAPRS, Vol. XXXVIII, Part 3/W8 – Paris, France, September 1-2, 2009
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However, sometimes a particle that does not represent a good
solution is going to be evaluated as if it did. For instance,
suppose that one of the particle clusters has a data vector that
is very close to its centroid, and another cluster has a lot of
data vectors that are not so close to the centroid. This is not a
very good solution, but giving the same weight to the cluster
with one data vector as the cluster with a lot of data vectors
can make it seem to be. Furthermore, this equation is not
going to reward the homogeneous solutions, that is, solutions
where the data vectors are well distributed along the clusters
(Esmin et al., 2008). To solve this problem Esmin et al.,
proposed the following equation, where the number of data
vectors belonging to each cluster is taken into account on the
calculation of the quality (Esmin et al., 2008):
3.2 PSO Clustering
For the purpose of this paper, define the following symbols: Nd
denotes the input dimension, i.e. the number of parameters of
each data vector; No denotes the number of data vectors to be
clustered; Nc denotes the number of cluster centroids (as
provided by the user), i.e. the number of clusters to be formed;
zp denotes the p-th data vector; mj denotes the centroid vector of
cluster j; nj is the number of data vectors in cluster j; Cj is the
subset of data vectors that form cluster j.
In the context of clustering, a single particle represents the Nc
cluster centroid vectors (Merwe, and Engelbrecht, 2003; Esmin
et al., 2008). That is, each particle is constructed as follows:
,…,
,…,
∑
where mij refers to the j-th cluster centroid vector of the i-th
particle in cluster Cij . Therefore, a swarm represents a number
of candidate clusters for the current data vectors. The fitness of
particles is easily measured as the quantization error (Merwe,
and Engelbrecht, 2003).
∑
∑
,
where d is defined in equation (1),
vectors belonging to cluster .
∑
⁄
,
(4)
where No is the number of data vectors to be clustered.
To take into account the distribution of the data among the
clusters, the equation can be changed to:
F
(3)
|
Such that, | | max
| | min
is the number of data
|
|
,…,
|
1
(5)
and
,…,
4. EXPERIMENTAL INVESTIGATIONS
Using the standard gbest PSO, data vectors can be clustered as
follows:
1.
2.
The airborne LIDAR data used in the experimental
investigations have been recorded with TopScan's Airborne
Laser Terrain Mapper system ALTM 1225 (TopScan, 2004).
The data are recorded in area of Rheine in Germany. Two
different patches with residential and industrial pattern were
selected in the available dataset. The selected areas were
suitable for the evaluation of the proposed classification
strategy because the required complexities (e.g. proximities of
different objects: building and tree) were available in the
image (Figure 1. a, b). The pixel size of the range images is
one meter per pixel. This reflects the average density of the
irregularly recorded 3D points which is fairly close to one per
m2. Intensity images for the first and last pulse data have been
also recorded and the intention was to use them too in the
experimental investigations. Figure (1) shows first- and lastpulse range images from the Rheine area. The impact of the
trees in the first- and last- pulse images can be easily
recognized by comparing the two images of this figure.
Initialize each particle to contain Nc randomly
selected cluster centroids.
For t = 1 to tmax do
i. For each particle i do
ii. For each data vector
a. calculate the Euclidean distance
,
to
all cluster centroids
to cluster
such that distance
b. assign
,
min
,…N
,
c. calculate the fitness using equation (3)
iii. Update the global best and local best positions
iv. Update the cluster centroids.
where tmax is the maximum number of iterations. The
population-based search of the PSO algorithm reduces the effect
that initial conditions has, as opposed to the K-means algorithm;
the search starts from multiple positions in parallel.
The first step in every clustering process is to extract the
feature image bands. The features of theses feature bands
should carry useful textural or surface related information to
differentiate between regions related to the surface. Several
features have been proposed for clustering of range data.
Axelsson (1999) employs the second derivatives to find
textural variations and Maas (1999) utilizes a feature vector
including the original height data, the Laplace operator,
maximum slope measures and others in order to classify the
data. In the following experiments we restrict to five types of
features:
However, the K-means algorithm tends to converge faster (after
less function evaluations) than the PSO, but usually with a less
accurate clustering (Omran et al., 2005). Merwe, and
Engelbrecht, showed that the performance of the PSO clustering
algorithm can further be improved by seeding the initial swarm
with the result of the K-means algorithm (Merwe, and
Engelbrecht, 2003). The hybrid algorithm first executes the Kmeans algorithm once. In this case the K-means clustering is
terminated when (1) the maximum number of iterations is
exceeded, or when (2) the average change in centroids vectors is
less that 0.0001 (a user specified parameter). The result of the
K-means algorithm is then used as one of the particles, while
the rest of the swarm is initialized randomly. The gbest PSO
algorithm as presented above is then executed.




LIDAR range data
The ratio between first and last pulse range images
Top-Hat filtered last pulse range image
Local height variation which is computed using a small
window (3*3) around a data sample.
 Last pulse Intensity
336
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a
b
c
d
e
f
a
c
b
d
e
f
Figure 2. Clustering results. a) Manual Digitization objects in
residential area. b) Manual Digitization objects in industrial
area. c) Clustering results of k-means in residential area. d)
Clustering results of k-means in industrial area. e) Clustering
results of PSO algorithm in residential area. f) Clustering
results of PSO algorithm in industrial area.
For both data sets, averages over 30 simulations are given. All
algorithms are run for 300 function evaluations, and the PSO
algorithms used 15 particles. For PSO, w = 0.72 and c1 = c2 =
1.49. These values were chosen to ensure good convergence
(Omran et al., 2005).
g
h
Figure 1. a) Aerial image of residential evaluation area. b)
Aerial image industrial evaluation area. c) First LIDAR range
data of residential area. d) First LIDAR range data of industrial
area. e) Second LIDAR range data of residential area. f) Second
LIDAR range data of industrial area. g) Overlaid manual
digitization objects in residential area. h) Overlaid manual
digitization objects in industrial Area
4.1 Accuracy Assessment
Comparative studies on clustering algorithms are difficult due
to lack of universally agreed upon quantitative performance
evaluation measures. Many similar works in the clustering
area use the classification error as the final quality
measurement; so in this research, we adopt a similar approach
(Zhong and Ghosh, 2003).
Evaluation of these two algorithms for clustering of the data sets
into three clusters (ground, tree, and building) is depicted in
Figure 2. Figures (2c) and (2d) show the k-means clustering
results and Figures (2e) and (2f) show the PSO clustering
algorithm results in two evaluation areas. Building class regions
are highlighted in red and vegetation class regions in green
colour in Figure 2. Visual inspections shows that vegetation
class is directly associated with vegetation, in particular trees,
bushes or forest and the B-class is mainly associated with
building regions.
In this paper, confusion matrix used to evaluate the true labels
and the labels returned by the clustering algorithms as the
quality assessment measure. Given some ground truth the
relation between the ''true'' classes and the classification result
can be quantified. With the clusters the same principle can be
applied. Mostly a much bigger number of clusters is then
related to the given ground truth classes to examine the quality
of the clustering algorithm. From the confusion matrix we
calculate the Kappa Coefficient (Cohen, 1960). The accuracy
measurements showing above, namely, the overall accuracy,
producer’s accuracy, and user’s accuracy, though quite simple
337
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to use, are based on either the principal diagonal, columns, or
rows of the confusion matrix only, which does not use the
information from the whole confusion matrix. A multivariate
index called the Kappa coefficient (Tso and Mather, 2009) has
found favour. The Kappa coefficient uses all of the information
in the confusion matrix in order for the chance allocation of
labels to be taken into consideration. The Kappa coefficient is
defined by:
∑
∑
∑
obtained with the PSO algorithm method is supported by
visual interpretation.
1
0.5
K‐Mean
PSO
0
(6)
Residental
Industrial
In this equation, k is the Kappa coefficient, r is the number of
columns (and rows) in a confusion matrix, xii is entry (i, i) of
the confusion matrix, xi+ and x+i are the marginal totals of row
i and column j, respectively, and N is the total number of
observations (Tso and Mather, 2009).
Figure 3. The value of Kappa coefficient, in two situations of
clustering by kemean and PSO.
Table 1 shows the confusion matrix and Kappa coefficient of kmeans and PSO algorithms clustering in residential dataset. The
Error matrix and Kappa coefficient of k-means and PSO
algorithms clustering in industrial dataset presented in Table 2.
This paper presented the capability of a new clustering method
based on the particle swarm optimization algorithm in object
extraction form LIDAR data. The method employs the PSO
algorithm to search for the set of cluster centres that
minimizes a given clustering metric. One of the advantages of
this method is that it does not become trapped at locally
optimal solutions. This is due to the ability of the PSO
algorithm to perform local and global search simultaneously.
Experimental results for different LIDAR data sets have
demonstrated that the PSO algorithm method produces better
performances than those of the k-means algorithm.
5. CONCLUSION
K-Means
Table 1. Error matrix and Kappa coefficient of k-means and
PSO algorithms clustering applied to residential area.
Building
Tree
Ground
Total
Building
64338
3561
54341
122240
Reference Data
Tree
Ground
1551
338
58692
5930
10509
290740
70752
297008
Total
66227
68183
355590
490000
One of the drawbacks of the artificial PSO algorithm is the
number of tunable parameters it employs. A possible line of
research, therefore, is to find ways to help the user choose
appropriate parameters.
PSO algorithms
Kappa coefficient = 0.6927
Building
Tree
Ground
Total
Reference Data
Tree
Ground
2473
6463
61356
5193
6803
286551
70632
298207
Kappa coefficient = 0.898
Building
114673
3022
3466
121161
Total
123609
69571
296820
490000
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